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## Homework Statement

The principal valueof the logarithmic function of a complex variable is defined to ave its argument in the range -pi < arg(z) < pi. By writing z = tan(w) in terms of exponentials, show that:

tan

^{-1}(z) = (1/2i)ln[(1 + iz)/(1 - iz)]

## The Attempt at a Solution

I have absolutely no idea where to start on this problem. My brain must be fried this week, but all I know how to do is write z = tan(w) in terms of exponentials.

z = (1/2i)(e

^{iw}+ e

^{-iw})/(e

^{iw}- e

^{iw})

Thanks!

Andrew